立方非线性微结构固体中的对称孤立波及存在条件

那仁满都拉; 额尔敦仓

doi:10.3879/j.issn.1000-0887.2014.11.004

立方非线性微结构固体中的对称孤立波及存在条件

doi: 10.3879/j.issn.1000-0887.2014.11.004

内蒙古民族大学物理与电子信息学院, 内蒙古通辽 028043

基金项目: 国家自然科学基金（11462019; 10862003）

详细信息

作者简介:
那仁满都拉（1963—），男，蒙古族，内蒙古通辽人，教授，博士，硕士生导师(通讯作者. E-mail: nrmdltl@126.com).

中图分类号: O331;O347
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- 被引次数: 0
出版历程
- 收稿日期: 2014-05-22
- 修回日期: 2014-06-22
- 刊出日期: 2014-11-18

Symmetric Solitary Waves and Their Existence Conditions in Cubic Nonlinear Microstructured Solids

College of Physics and Electronic Information, Inner Mongolia University for the Nationalities, Tongliao, Inner Mongolia 028043, P.R.China

Funds: The National Natural Science Foundation of China（11462019; 10862003）

摘要

摘要: 考虑固体材料的宏观尺度立方非线性效应、微尺度立方非线性效应以及微尺度频散效应并根据修正的Mindlin理论，建立了一维微结构固体中纵波传播的一种新模型.用动力系统的定性分析方法，证明了适当条件下立方非线性微结构固体中可存在对称钟型孤立波和反钟型孤立波，并给出了两种孤立波的存在条件.用数值方法分析了微尺度立方非线性效应对钟型与反钟型孤立波的影响，结果显示随着微尺度非线性效应的增强（或负增强），两种孤立波的宽度变窄（或变宽）而幅度保持不变.
- Mindlin理论 /
- 微结构固体 /
- 孤立波 /
- 存在条件
Abstract: In view of the macroscale cubic nonlinear effect, the microscale cubic nonlinear effect and the microscale dispersion effect of solid materials, a new model for the longitudinal wave propagation in 1D microstructured solids was established based on the modified Mindlin theory. The qualitative analysis method was applied to the dynamical system, the existence of symmetric bell and anti-bell type solitary waves in the cubic nonlinear microstructured solid was proved under appropriate conditions, and the existence conditions of the 2 solitary waves were given. The microscale cubic nonlinear effect on the bell and anti-bell type solitary waves was analyzed with the numerical method. The results indicate that the widths of the 2 solitary waves decreases (or increases) with the rise (or fall) of the microscale nonlinear effect while the amplitudes of the 2 solitary waves remain unchanged.
- Mindlin theory /
- microstructured solid /
- solitary wave /
- existence condition

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参考文献(13)

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